The nucleus of an atom carries the essential mass of the atom despite its small size because it contains the majority of the atom's mass in the form of protons and neutrons.
Protons and neutrons are subatomic particles that make up the nucleus. Protons have a positive charge, while neutrons have no charge. Electrons, which are negatively charged, orbit around the nucleus in regions known as electron shells or energy levels.
The mass of a proton is approximately 1 atomic mass unit (u), and the mass of a neutron is also around 1 u. In comparison, the mass of an electron is extremely small, only about 0.0005 u. Therefore, the mass of electrons is negligible compared to the mass of protons and neutrons.
The reason the nucleus carries most of the atom's mass despite its small size is due to the relative masses of these particles. The mass of a proton or neutron is roughly 2,000 times greater than the mass of an electron. Since protons and neutrons are tightly packed within the nucleus, their combined mass dominates the overall mass of the atom.
The size of the nucleus is much smaller than the overall size of the atom because most of the atom is occupied by the electron clouds or electron shells. Electrons are much lighter than protons and neutrons, and their orbits extend relatively far from the nucleus. The electron shells determine the atom's size and how it interacts with other atoms.
In summary, the nucleus carries the essential mass of the atom because it contains the relatively heavy protons and neutrons, while the electrons, which have much smaller masses, occupy larger regions around the nucleus.